Reports that say that something hasn’t happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns — the ones we don’t know we don’t know. And if one looks throughout the history of our country and other free countries, it is the latter category that tends to be the difficult ones.
Donald Rumsfeld made this marvelous quote in a remarkably cynical way, as a way to avoid answering a question. It has been a source of much discussion, a recent documentary
and the most obvious cultural touchstone for uncertainty quantification. He also forgot the most important category, the unknown known, and the axiomatic things that we don’t even question or think about. For Rumsfeld it was the unknown knowns that more than anything drove us to war and influenced decisions in ways that we never fully acknowledged. All of us have this sort of blind side, the things that drive our decisions that we don’t even think about.
So what our some of the unknown knowns for that I deal with?
For example at Sandia the Finite Element Method is an unknown known. It is applied without thought or debate, it is just assumed to be the method of choice. There is
no discussion or thought with the choice as it is applied axiomatically. Even when non-finite element methods are used, they are called a finite element discretization as a way to smooth the way to acceptance.
I’ve noticed that our viewpoint on modeling in the continuum hypothesis is similarly axiomatic. In many ways it is remarkable that we continue to solve problems in exactly the same philosophical way that Von Neumann envisioned even though computers have advanced by a factor of more than quadrillion in power. In some cases we don’t include details of physics that now come into view such as grain structure, texture, anisotropic properties, etc. In hydrocodes we simply “paint” materials into regions and apply homogeneous properties even though the materials are definitely heterogeneous at the scale of the mesh. Generally speaking, the changes necessary to model things correctly is barely on the technical agenda. These features are more prevalent in
weather and climate where the differences in the physics are more obvious. We know that the asymptotics differ and the equations need to change. In continuum mechanics this is beginning to dawn on people too.
I suppose it is tempting, if the only tool you have is a hammer, to treat everything as if it were a nail.
Our society has many of its own axioms, such as “American exceptionalism” which is either axiomatically good or bad depending on who you talk to. The view of socialism, free enterprise, and liberalism all fall prey to the unknown known. It has become the prevalent way of managing complexity and simply assuming the answer is easier than thinking about the inherent complexity of things. This thought process is the heart of racism, sexism, gay bashing and a host of societies greatest ills. By simply assuming certain things to be true without question makes life easy, but it also allows people to do terrible things with complete justification. This brings us back to Rumsfeld.
Your assumptions are your windows on the world. Scrub them off every once in a while, or the light won’t come in.